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Unformatted text preview: STAT503 Spring 2007 Lecture Notes: Chapter 9 1 Chapter 9: Comparison of Paired Samples November 4, 2008 9.1 Introduction Observations occur in pairs such as: I as identical twins, I two observations on the same individual (two days, two sides, before/after) I a two-treatment block design where each block is of size 2 (subjects matched in pairs for similar age, sex, profession, disease status, other extraneous variables) 9.2 The Paired Sample t-test and Confidence Interval This is a combination of two things you already know. I Two sample and one sample t-tests (also C.I.s) You must recognize that the study is a paired design. Do the hypothesis steps like a 2-independent sample t-test (steps 14 and step 10). Calculate the differences D = Y 1- Y 2 . Do the t calculations for the differences like a 1-sample t-test (steps 59). Directionality works as before. It is the observed differences that we wish to analyze. n is the number of pairs in the sample. Example: Have 12 fruit flies from 6 different lines (2 of each) grown in vials at two different temperatures. After a specified time for development, count the number of bristles on each fly. We think that bristle number has approximately a normal distribution, but flies from the same line should have similar bristle numbers. Chapter9.tex; Last Modified: November 4, 2008 (W. Sharabati) STAT503 Spring 2007 Lecture Notes: Chapter 9 2 So we will look at the difference in bristle number between two flies of the same line. Block = line Treatment = temperature Have 12 observations but they occur in 6 pairs so n = 6. Cold Warm Difference Line y 1 y 2 d = y 1- y 2 1 24 25-1 2 41 40 +1 3 44 46-2 4 30 31-1 5 28 31-3 6 43 43 mean 35 36-1.0 s 1.414 SE s n = 0 . 577 Does temperature affect the number of bristles on fruit flies? Let 1 and 2 be the mean bristle number for flies grown at the colder and warmer temperatures, respectively H : 1 = 2 ; the mean bristle number is the same for both temperatures H A : 1 6 = 2 ; the mean bristle number is different at the two temperatures Use a non-directional paired sample t-test....
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- Spring '08
- Normal Distribution, two days, Student's t-test, #pairs, W. Sharabati